In recent years, in an internal combustion engine mounted in a vehicle, a catalyst such as a three-way catalyst for purifying an exhaust gas and an air-fuel ratio sensor for detecting an air-fuel ratio of the exhaust gas representing air-fuel mixture are installed in an exhaust pipe. An air-fuel ratio feedback control to control a fuel injection amount of a fuel injection valve is performed so that the air-fuel ratio of the exhaust gas detected by the air-fuel ratio sensor is controlled to become a target air-fuel ratio (purification window of catalyst), and an exhaust gas purification efficiency of the catalyst is raised.
In such an air-fuel ratio feedback control, as disclosed in U.S. Pat. No. 6,397,830 B1 (JP-A-2001-90584), an air-fuel ratio control model simulating a control object from a fuel injection valve to an air-fuel ratio sensor is constructed. A response time constant of the air-fuel ratio control model is changed in accordance with an engine operation state, and a control gain is changed in accordance with this response time constant so that the characteristic of the air-fuel ratio control model is changed in accordance with the engine operation state. While the stability of the air-fuel ratio feedback control is secured in all the operation region, the response of the air-fuel ratio feedback control over the change of the engine operation state can be improved.
However, in an internal combustion engine including multiple cylinders, variation occurs in the operation states of the respective cylinders due to individual differences of the respective cylinders (parts tolerances, assembly tolerances, etc.), secular change, and the like. When the variations in the operation states among the cylinders are large, the fluctuation of air-fuel ratio sensor output in a cycle becomes large by the influence. In the air-fuel ratio feedback control of U.S. Pat. No. 6,397,830 B1, the variation among the cylinders is not considered. Even in a state where the variation among the cylinders is large, when the engine operation states are the same, the same control gain is set. Therefore, when the fluctuation of the air-fuel ratio sensor output becomes large by the influence of the variation among the cylinders, the fluctuation of an air-fuel ratio feedback correction amount becomes large in accordance with that. Thus, the stability of the air-fuel ratio feedback control is no ensured.